The other week I used the example of a late-Medieval instrument, the Vielle, as a practical example of the overlap of music and musical proportion. Jerome of Moravia provided the tuning for the Vielle in the 13th Century. We used just one tuning for the arrangement of the body of our example Vielle, though all three he describes are fundamentally similar.
d G g d’ d’ d G g d’ g’ G G d c’ c’
The first tuning is considered best for Church Music. The “leftmost” d string is actually a drone string, meaning it does not get fingered during the playing of the instrument. Every draw of the bow across the strings (which are on a flat fretboard making it neigh impossible to play a single string at a time) results in the constant “drone” of a musical fifth in relation to the tuning of the instrument. The other two tunings are for secular playing, and actually do not have the separate drone string. In the first and second case, the instrument is tuned to an open playing of fifths and octaves. The third tuning open playing of fourths is added at the loss of open perfect fifths. As we look at the individual strings, we see that they are generally composed of variations of 1:1, 2:1, 4:3, and 3:2 in relation to the others on the instrument. Other notes are achieved by stopping the strings at various distances.
Medieval Music Theorists (and modern students of such) can readily identify the first two tunings as the Hypomixolydian Diatonic Scale. This scale is a variation of the scale attributed to Greek Poet Sappho in the 7th Century BCE (by way of Boethius’ translation of Claudius Ptolemy’s “Harmonics,” 2nd Cen CE).
There is only one interval missing in the open tunings from the diatonic scale, and the Tetractys, the Second (9:8). This one is easily attainable with a single fingering on the fretboard. The variation of a Second is so narrow, however, we might consider it an accent required to complete the scale. And should we apply this to design, we find a place for all those little things – a foot or finial at the end of a stile, the thickness of a mutin or the overlapping lip of a chest, the width of a moulding profile… Whether we accurately measure such an element (with dividers and sector) or get it relatively close by eye, we have added that last “musical” element to complete the octave.
And as a fun aside, when tuned to a diatonic scale in perfect fifths like these instruments, any fingering position will sound “good” when played. It’s actually difficult and takes effort to sound an “off” note or chord.